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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions. In R , function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization.
Support for multi-dimensional arrays may also be provided by external libraries, which may even support arbitrary orderings, where each dimension has a stride value, and row-major or column-major are just two possible resulting interpretations. Row-major order is the default in NumPy [19] (for Python).
For example, with N = M the number of fixed points is simply N (the diagonal of the matrix). If N − 1 and M − 1 are coprime, on the other hand, the only two fixed points are the upper-left and lower-right corners of the matrix. The number of cycles of any length k>1 is given by (Cate & Twigg, 1977):
Prior to Python 3, there were two kinds of integral numbers: traditional fixed size integers and "long" integers of arbitrary size. The conversion to "long" integers was performed automatically when required, and thus the programmer usually didn't have to be aware of the two integral types.
The number of elements used by the dynamic array contents is its logical size or size, while the size of the underlying array is called the dynamic array's capacity or physical size, which is the maximum possible size without relocating data. [2] A fixed-size array will suffice in applications where the maximum logical size is fixed (e.g. by ...
Some array data structures do not reallocate storage, but do store a count of the number of elements of the array in use, called the count or size. This effectively makes the array a dynamic array with a fixed maximum size or capacity; Pascal strings are examples of this.